Inertial confinement fusion (ICF) targets designed to achieve ignition must meet strict surface smoothness and sphericity requirements. One potentially valuable method for evaluating the quality of these targets is resonant ultrasound spectroscopy (RUS). When applied to simple geometries, such as layered spheres or rectangular parallelepipeds, RUS may yield significant information about alloy homogeneity, elastic constants, cavity geometry, the presence of gross defects such as cracking or hemishell bonding problems, and properties of interior fluids. The strengths of RUS techniques for ICF target characterization include applicability at all temperatures of interest with a single apparatus, high sensitivity in frequency spectral measurements, and the inherent acoustic indifference to optically opaque samples. Possible applications and the limitations of RUS methods for examining layer geometry and material properties are addressed. Preliminary room temperature experiments with a deuterium-filled aluminum shell are used to evaluate the utility of many of the described applications. The frequency spectrum compares favorably with theory and displays measurable mode splitting, acoustic-mode resonance widths indicative of cavity boundary dissipative mechanisms, and low-Q elastic modes. The acoustic cavity resonance structure confirms the internal gas density and is used to calculate the two lowest even-order cavity boundary perturbation amplitudes.